Properties and Iterative Methods for the Q-Lasso
We introduce the Q-lasso which generalizes the well-known lasso of Tibshirani (1996) with Q a closed convex subset of a Euclidean m-space for some integer m≥1. This set Q can be interpreted as the set of errors within given tolerance level when linear measurements are taken to recover a signal/image...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/250943 |
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| author | Maryam A. Alghamdi Mohammad Ali Alghamdi Naseer Shahzad Hong-Kun Xu |
| author_facet | Maryam A. Alghamdi Mohammad Ali Alghamdi Naseer Shahzad Hong-Kun Xu |
| author_sort | Maryam A. Alghamdi |
| collection | DOAJ |
| description | We introduce the Q-lasso which generalizes the well-known lasso of Tibshirani (1996)
with Q a closed convex subset of a Euclidean m-space for some integer m≥1. This set Q can be interpreted as the set of errors within given tolerance level when linear measurements
are taken to recover a signal/image via the lasso. Solutions of the Q-lasso depend on a tuning parameter γ. In this paper, we obtain basic properties of the solutions as a function of γ. Because of ill posedness, we also apply l1-l2 regularization to the Q-lasso. In addition, we discuss iterative methods for solving the Q-lasso which include the proximal-gradient algorithm and the projection-gradient algorithm. |
| format | Article |
| id | doaj-art-1e4a7075cdc949879969b48a1c197906 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1e4a7075cdc949879969b48a1c1979062025-02-03T01:31:30ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/250943250943Properties and Iterative Methods for the Q-LassoMaryam A. Alghamdi0Mohammad Ali Alghamdi1Naseer Shahzad2Hong-Kun Xu3Department of Mathematics, Sciences Faculty for Girls, King Abdulaziz University, P.O. Box 4087, Jeddah 21491, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaDepartment of Mathematics, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi ArabiaWe introduce the Q-lasso which generalizes the well-known lasso of Tibshirani (1996) with Q a closed convex subset of a Euclidean m-space for some integer m≥1. This set Q can be interpreted as the set of errors within given tolerance level when linear measurements are taken to recover a signal/image via the lasso. Solutions of the Q-lasso depend on a tuning parameter γ. In this paper, we obtain basic properties of the solutions as a function of γ. Because of ill posedness, we also apply l1-l2 regularization to the Q-lasso. In addition, we discuss iterative methods for solving the Q-lasso which include the proximal-gradient algorithm and the projection-gradient algorithm.http://dx.doi.org/10.1155/2013/250943 |
| spellingShingle | Maryam A. Alghamdi Mohammad Ali Alghamdi Naseer Shahzad Hong-Kun Xu Properties and Iterative Methods for the Q-Lasso Abstract and Applied Analysis |
| title | Properties and Iterative Methods for the Q-Lasso |
| title_full | Properties and Iterative Methods for the Q-Lasso |
| title_fullStr | Properties and Iterative Methods for the Q-Lasso |
| title_full_unstemmed | Properties and Iterative Methods for the Q-Lasso |
| title_short | Properties and Iterative Methods for the Q-Lasso |
| title_sort | properties and iterative methods for the q lasso |
| url | http://dx.doi.org/10.1155/2013/250943 |
| work_keys_str_mv | AT maryamaalghamdi propertiesanditerativemethodsfortheqlasso AT mohammadalialghamdi propertiesanditerativemethodsfortheqlasso AT naseershahzad propertiesanditerativemethodsfortheqlasso AT hongkunxu propertiesanditerativemethodsfortheqlasso |